Divisor function Totally Explained

Everything about Divisor Function totally explained

In mathematics, and specifically in number theory, a divisor function is an arithmetical function related to the divisors of an integer. When referred to as the divisor function, it counts the number of divisors of an integer. It appears in a number of remarkable identities, including relationships on the Riemann zeta function and the Eisenstein series of modular forms. Divisor functions were studied by Ramanujan, who gave a number of important congruences and identities.
A related function is the divisor summatory function, which, as the name implies, is a sum over the divisor function.

Definition

The sum of positive divisors function σ_x(n) is defined as the sum of the x^th powers of the positive divisors of n, or ť

sigma_

for every natural number n, where

H_n

is the nth harmonic number.

Further Information

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